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Unformatted text preview: Chapter 12 Production with Multiple Inputs In Chapter 11, we developed some of the basic building blocks of the producer model but we limited ourselves to the case of a single input being used to produce a single output. 1 From the outset, we did not hide the fact that such simple production processes rarely exist in the world, except perhaps in the short run where producers have little control over various inputs (like factory space) and can vary only a single input when trying to adjust production. But restricting ourselves to the single input/single output setting allowed us to depict the building blocks of the producer model in two-dimensional graphs of production plans, with production choice sets forming the technological constraint faced by producers and isoprofit curves depicting their tastes for profit. This chapter will now focus on how we can extend the model to multiple inputs two in the case of our graphical development in Section A and more in our mathematical approach of Section B. Modeling a two input/one output production process will then either involve graphs with three dimensional objects or the utilization of shortcuts that permit us to graph these objects in two dimensions. This will allow us to consider in Chapter 13 how producers substitute between different inputs as input prices change, and how short run decisions for producers differ from long run decisions. 12A An Intuitive Development of the 2-Input Model The basic building block of the producer model extends straightforwardly from the single input to the two input case. Production plans , previously defined as points in a 2-dimensional space indicating how much input (labor) the plan calls for to produce a certain level of output ( x ), are now defined as points in 3-dimensions which indicate how much of each of the two inputs the plan proposes to use in the production of a certain level of output. For convenience, we will once again often call one input labor (denoted ), and we will usually call the other input capital (denoted k ). Clearly we are still simplifying the real world a lot leaving out (until Section B) such important inputs as land and neglecting to distinguish between different types of labor and capital. 1 Chapter 11 is required reading for this chapter. No material from chapters prior to chapter 11 is directly used in this chapter. However, as chapter 11, this chapter contains frequent analogies to the consumer model and particularly to material covered in chapter 2, chapters 4 through 6. The final part of the B section also draws analogies to chapter 10. 306 Chapter 12. Production with Multiple Inputs A production plan A , previously defined as a point ( A ,x A ) is therefore now defined as a point ( A ,k A ,x A ). We will continue to talk about the labor input as expressed in hours of labor input and can thus continue to express its price in the labor market as the hourly wage rate w . Similarly,....
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